Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is g and that on the surface of the new planet is g', then :
g'=3g
g'=\(\frac{g}{9}\)
g'=9g
g'=\(\frac{g}{3}\)
The Correct Option is A
Solution and Explanation
Let the mass and radius of the new planet be M′ and R′, then for same density as earth,
R′=3R
M′=27M
we know M\(\propto\)V, where V\(\propto\)R3
For Earth
g=\(\frac{GM}{R^2}\) (1)
and for new planet
g'=\(\frac{GM'}{R^2}\)
=\(\frac{G(27M)}{(3R)^2}\)
=\(3\bigg(\frac{GM}{R^2}\bigg)\)=3g
\(\Rightarrow\) g'=3g
Therefore, the correct option is (A): g'=3g
Top Questions on Gravitation
- A body of mass $ 1.5 \, \text{kg} $ is dropped from a height of $ 20 \, \text{m} $. What is its speed just before hitting the ground? (Assume $ g = 9.8 \, \text{m/s}^2 $)
- MHT CET - 2025
- Physics
- Gravitation
- What is the gravitational force between two objects of masses \( m_1 = 10 \, \text{kg} \) and \( m_2 = 20 \, \text{kg} \), separated by a distance of \( r = 5 \, \text{m} \)? (Gravitational constant \( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))
- MHT CET - 2025
- Physics
- Gravitation
- The value of \( g \) at height \( h \) above Earth's surface is \( \frac{g}{\sqrt{3}} \). Find \( h \) in terms of the radius of the Earth.
- MHT CET - 2025
- Physics
- Gravitation
- At a height \( h \) above the Earth's surface, the acceleration due to gravity becomes \( \frac{g}{\sqrt{3}} \). What is the value of \( h \) in terms of the Earth's radius \( R \)?
- MHT CET - 2025
- Physics
- Gravitation
- If \( r_1, v_1, L_1 \) and \( r_2, v_2, L_2 \) are radii, velocities, and angular momenta of a planet at perihelion and aphelion of its elliptical orbit around the Sun respectively, then
- KCET - 2025
- Physics
- Gravitation
Questions Asked in NEET exam
- A bob is whirled in a horizontal plane by means of a string with an initial speed of ω rpm. The tension in the string is T. If speed becomes 2ω while keeping the same radius, the tension in the string becomes:
Identify the major product C formed in the following reaction sequence:
- NEET (UG) - 2024
- Chemical Reactions
- In an electrical circuit, the voltage is measured as V = (200 ± 4) volt and the current is measured as I = (20 ± 0.2) A. The value of the resistance is:
- NEET (UG) - 2024
- Current electricity
- What is the fate of a piece of DNA carrying only gene of interest which is transfered in to an alien organism?
A. The piece of DNA would be able to multiply itself independently in the progeny cells of the organism.
B. It may get integrated into the genome of the recipient.
C. It may multiple and be inherited along with the host DNA.
D. The alien piece of DNA is not an integral part of chromasame.
E. It shows ability to replicate.
Choose the correct answer from the options given below: - The magnetic moment of an iron bar is M. It is now bent in such a way that it forms an arc section of a circle subtending an angle of 60° at the centre. The magnetic moment of this arc section is
- NEET (UG) - 2024
- Magnetic moment
Concepts Used:
Gravitation
In mechanics, the universal force of attraction acting between all matter is known as Gravity, also called gravitation, . It is the weakest known force in nature.
Newton’s Law of Gravitation
According to Newton’s law of gravitation, “Every particle in the universe attracts every other particle with a force whose magnitude is,
- F ∝ (M1M2) . . . . (1)
- (F ∝ 1/r2) . . . . (2)
On combining equations (1) and (2) we get,
F ∝ M1M2/r2
F = G × [M1M2]/r2 . . . . (7)
Or, f(r) = GM1M2/r2
The dimension formula of G is [M-1L3T-2].